The Study of A System of Non-Homogeneous Equations Using Matrix Exponential Method and Analysis With Scilab Software 6.1.1

Abstract

Abstract The study for a system of non-homogeneous equations (coupled differential equations) with initial conditions using Matrix Exponential Method has been done through Scilab software as well as manually. We observe that both the procedures for the equations have been satisfied with the initial conditions. Eigen values and corresponding eigen vectors have been determined to get the complete solutions; and the solutions for x and y also have been found manually. The graphs are plotted with Scilab software 6.1.1. A linear relation between x & y is observed by the new outcomes when they plotted. The study of variation of x, y with t shows the curves increase linearly for limited values of t also the study between t, x+y & t, x-y shows that the curves of both are the mirror image about x-axis. There are much more applications of matrix exponential method in science, engineering and computational fields.